A Card Number is the eight-digit number that most cards have on the bottom-left corner on the card (certain cards, such as "Gate Guardian", do not have this card number).
Card Numbers, while serving no real purpose in the actual game, do serve a purpose in video games. By entering a card number found on a given card (usually in a "Password" selection screen), a player may obtain that card for their virtual collection, although various restrictions are placed on this depending on the game. In most games, this can only be done once per card. In some games entering the code will get the player the card for free, while in others the player must pay in-game currency to do so. In most of the latest games, players must also have to have the card they are trying to get in their card list, which either involves owning the card, or owning most of the cards in the set the card comes in.
Passcodes are similar to Card Numbers, except they can contain a mix of letters and numbers, and are used in only a handful of games.